LMFDB - Embedded newform 5070.2.a.bo.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5070,2,Mod(1,5070)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5070, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5070.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5070.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$40.4841538248$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.80194$ of defining polynomial
Character	$\chi$	$=$	5070.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +4.80194 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +4.80194 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +2.55496 q^{11} +1.00000 q^{12} -4.80194 q^{14} -1.00000 q^{15} +1.00000 q^{16} -3.02715 q^{17} -1.00000 q^{18} -3.89977 q^{19} -1.00000 q^{20} +4.80194 q^{21} -2.55496 q^{22} -1.64310 q^{23} -1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{27} +4.80194 q^{28} +5.07606 q^{29} +1.00000 q^{30} +5.44504 q^{31} -1.00000 q^{32} +2.55496 q^{33} +3.02715 q^{34} -4.80194 q^{35} +1.00000 q^{36} +7.51573 q^{37} +3.89977 q^{38} +1.00000 q^{40} -5.89977 q^{41} -4.80194 q^{42} -10.1468 q^{43} +2.55496 q^{44} -1.00000 q^{45} +1.64310 q^{46} +6.42758 q^{47} +1.00000 q^{48} +16.0586 q^{49} -1.00000 q^{50} -3.02715 q^{51} -6.91185 q^{53} -1.00000 q^{54} -2.55496 q^{55} -4.80194 q^{56} -3.89977 q^{57} -5.07606 q^{58} +7.60925 q^{59} -1.00000 q^{60} +9.65279 q^{61} -5.44504 q^{62} +4.80194 q^{63} +1.00000 q^{64} -2.55496 q^{66} +0.929312 q^{67} -3.02715 q^{68} -1.64310 q^{69} +4.80194 q^{70} +14.9487 q^{71} -1.00000 q^{72} +14.1129 q^{73} -7.51573 q^{74} +1.00000 q^{75} -3.89977 q^{76} +12.2687 q^{77} -5.40581 q^{79} -1.00000 q^{80} +1.00000 q^{81} +5.89977 q^{82} +4.33513 q^{83} +4.80194 q^{84} +3.02715 q^{85} +10.1468 q^{86} +5.07606 q^{87} -2.55496 q^{88} -16.8267 q^{89} +1.00000 q^{90} -1.64310 q^{92} +5.44504 q^{93} -6.42758 q^{94} +3.89977 q^{95} -1.00000 q^{96} +17.9855 q^{97} -16.0586 q^{98} +2.55496 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 10 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 10 * q^7 - 3 * q^8 + 3 * q^9	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 10 q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{10} + 8 q^{11} + 3 q^{12} - 10 q^{14} - 3 q^{15} + 3 q^{16} - 3 q^{17} - 3 q^{18} + 11 q^{19} - 3 q^{20} + 10 q^{21} - 8 q^{22} - 9 q^{23} - 3 q^{24} + 3 q^{25} + 3 q^{27} + 10 q^{28} + 3 q^{30} + 16 q^{31} - 3 q^{32} + 8 q^{33} + 3 q^{34} - 10 q^{35} + 3 q^{36} + 10 q^{37} - 11 q^{38} + 3 q^{40} + 5 q^{41} - 10 q^{42} - 3 q^{43} + 8 q^{44} - 3 q^{45} + 9 q^{46} + 3 q^{47} + 3 q^{48} + 17 q^{49} - 3 q^{50} - 3 q^{51} - 17 q^{53} - 3 q^{54} - 8 q^{55} - 10 q^{56} + 11 q^{57} + 11 q^{59} - 3 q^{60} + 11 q^{61} - 16 q^{62} + 10 q^{63} + 3 q^{64} - 8 q^{66} + 15 q^{67} - 3 q^{68} - 9 q^{69} + 10 q^{70} + 13 q^{71} - 3 q^{72} - q^{73} - 10 q^{74} + 3 q^{75} + 11 q^{76} + 29 q^{77} - 3 q^{79} - 3 q^{80} + 3 q^{81} - 5 q^{82} + 12 q^{83} + 10 q^{84} + 3 q^{85} + 3 q^{86} - 8 q^{88} + q^{89} + 3 q^{90} - 9 q^{92} + 16 q^{93} - 3 q^{94} - 11 q^{95} - 3 q^{96} - 6 q^{97} - 17 q^{98} + 8 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 10 * q^7 - 3 * q^8 + 3 * q^9 + 3 * q^10 + 8 * q^11 + 3 * q^12 - 10 * q^14 - 3 * q^15 + 3 * q^16 - 3 * q^17 - 3 * q^18 + 11 * q^19 - 3 * q^20 + 10 * q^21 - 8 * q^22 - 9 * q^23 - 3 * q^24 + 3 * q^25 + 3 * q^27 + 10 * q^28 + 3 * q^30 + 16 * q^31 - 3 * q^32 + 8 * q^33 + 3 * q^34 - 10 * q^35 + 3 * q^36 + 10 * q^37 - 11 * q^38 + 3 * q^40 + 5 * q^41 - 10 * q^42 - 3 * q^43 + 8 * q^44 - 3 * q^45 + 9 * q^46 + 3 * q^47 + 3 * q^48 + 17 * q^49 - 3 * q^50 - 3 * q^51 - 17 * q^53 - 3 * q^54 - 8 * q^55 - 10 * q^56 + 11 * q^57 + 11 * q^59 - 3 * q^60 + 11 * q^61 - 16 * q^62 + 10 * q^63 + 3 * q^64 - 8 * q^66 + 15 * q^67 - 3 * q^68 - 9 * q^69 + 10 * q^70 + 13 * q^71 - 3 * q^72 - q^73 - 10 * q^74 + 3 * q^75 + 11 * q^76 + 29 * q^77 - 3 * q^79 - 3 * q^80 + 3 * q^81 - 5 * q^82 + 12 * q^83 + 10 * q^84 + 3 * q^85 + 3 * q^86 - 8 * q^88 + q^89 + 3 * q^90 - 9 * q^92 + 16 * q^93 - 3 * q^94 - 11 * q^95 - 3 * q^96 - 6 * q^97 - 17 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.00000	−0.408248
$7$	4.80194	1.81496	0.907481	−	0.420093i	$-0.138003\pi$
$7$	4.80194	1.81496	0.907481	+	0.420093i	$0.138003\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	2.55496	0.770349	0.385174	−	0.922844i	$-0.374141\pi$
$11$	2.55496	0.770349	0.385174	+	0.922844i	$0.374141\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	−4.80194	−1.28337
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−3.02715	−0.734191	−0.367096	−	0.930183i	$-0.619648\pi$
$17$	−3.02715	−0.734191	−0.367096	+	0.930183i	$0.619648\pi$
$18$	−1.00000	−0.235702
$19$	−3.89977	−0.894669	−0.447335	−	0.894367i	$-0.647627\pi$
$19$	−3.89977	−0.894669	−0.447335	+	0.894367i	$0.647627\pi$
$20$	−1.00000	−0.223607
$21$	4.80194	1.04787
$22$	−2.55496	−0.544719
$23$	−1.64310	−0.342611	−0.171305	−	0.985218i	$-0.554798\pi$
$23$	−1.64310	−0.342611	−0.171305	+	0.985218i	$0.554798\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	0	0
$27$	1.00000	0.192450
$28$	4.80194	0.907481
$29$	5.07606	0.942601	0.471301	−	0.881973i	$-0.343785\pi$
$29$	5.07606	0.942601	0.471301	+	0.881973i	$0.343785\pi$
$30$	1.00000	0.182574
$31$	5.44504	0.977958	0.488979	−	0.872295i	$-0.337369\pi$
$31$	5.44504	0.977958	0.488979	+	0.872295i	$0.337369\pi$
$32$	−1.00000	−0.176777
$33$	2.55496	0.444761
$34$	3.02715	0.519151
$35$	−4.80194	−0.811676
$36$	1.00000	0.166667
$37$	7.51573	1.23558	0.617789	−	0.786344i	$-0.288029\pi$
$37$	7.51573	1.23558	0.617789	+	0.786344i	$0.288029\pi$
$38$	3.89977	0.632627
$39$	0	0
$40$	1.00000	0.158114
$41$	−5.89977	−0.921390	−0.460695	−	0.887559i	$-0.652400\pi$
$41$	−5.89977	−0.921390	−0.460695	+	0.887559i	$0.652400\pi$
$42$	−4.80194	−0.740955
$43$	−10.1468	−1.54737	−0.773683	−	0.633573i	$-0.781587\pi$
$43$	−10.1468	−1.54737	−0.773683	+	0.633573i	$0.781587\pi$
$44$	2.55496	0.385174
$45$	−1.00000	−0.149071
$46$	1.64310	0.242262
$47$	6.42758	0.937559	0.468780	−	0.883315i	$-0.344694\pi$
$47$	6.42758	0.937559	0.468780	+	0.883315i	$0.344694\pi$
$48$	1.00000	0.144338
$49$	16.0586	2.29409
$50$	−1.00000	−0.141421
$51$	−3.02715	−0.423885
$52$	0	0
$53$	−6.91185	−0.949416	−0.474708	−	0.880143i	$-0.657446\pi$
$53$	−6.91185	−0.949416	−0.474708	+	0.880143i	$0.657446\pi$
$54$	−1.00000	−0.136083
$55$	−2.55496	−0.344510
$56$	−4.80194	−0.641686
$57$	−3.89977	−0.516537
$58$	−5.07606	−0.666520
$59$	7.60925	0.990640	0.495320	−	0.868711i	$-0.335051\pi$
$59$	7.60925	0.990640	0.495320	+	0.868711i	$0.335051\pi$
$60$	−1.00000	−0.129099
$61$	9.65279	1.23591	0.617957	−	0.786212i	$-0.287961\pi$
$61$	9.65279	1.23591	0.617957	+	0.786212i	$0.287961\pi$
$62$	−5.44504	−0.691521
$63$	4.80194	0.604987
$64$	1.00000	0.125000
$65$	0	0
$66$	−2.55496	−0.314494
$67$	0.929312	0.113534	0.0567668	−	0.998387i	$-0.481921\pi$
$67$	0.929312	0.113534	0.0567668	+	0.998387i	$0.481921\pi$
$68$	−3.02715	−0.367096
$69$	−1.64310	−0.197806
$70$	4.80194	0.573941
$71$	14.9487	1.77408	0.887042	−	0.461690i	$-0.152757\pi$
$71$	14.9487	1.77408	0.887042	+	0.461690i	$0.152757\pi$
$72$	−1.00000	−0.117851
$73$	14.1129	1.65179	0.825895	−	0.563824i	$-0.190670\pi$
$73$	14.1129	1.65179	0.825895	+	0.563824i	$0.190670\pi$
$74$	−7.51573	−0.873686
$75$	1.00000	0.115470
$76$	−3.89977	−0.447335
$77$	12.2687	1.39815
$78$	0	0
$79$	−5.40581	−0.608202	−0.304101	−	0.952640i	$-0.598356\pi$
$79$	−5.40581	−0.608202	−0.304101	+	0.952640i	$0.598356\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	5.89977	0.651521
$83$	4.33513	0.475842	0.237921	−	0.971285i	$-0.423534\pi$
$83$	4.33513	0.475842	0.237921	+	0.971285i	$0.423534\pi$
$84$	4.80194	0.523934
$85$	3.02715	0.328340
$86$	10.1468	1.09415
$87$	5.07606	0.544211
$88$	−2.55496	−0.272359
$89$	−16.8267	−1.78363	−0.891813	−	0.452404i	$-0.850566\pi$
$89$	−16.8267	−1.78363	−0.891813	+	0.452404i	$0.850566\pi$
$90$	1.00000	0.105409
$91$	0	0
$92$	−1.64310	−0.171305
$93$	5.44504	0.564625
$94$	−6.42758	−0.662955
$95$	3.89977	0.400108
$96$	−1.00000	−0.102062
$97$	17.9855	1.82615	0.913077	−	0.407788i	$-0.133700\pi$
$97$	17.9855	1.82615	0.913077	+	0.407788i	$0.133700\pi$
$98$	−16.0586	−1.62216
$99$	2.55496	0.256783
$100$	1.00000	0.100000
$101$	−15.7453	−1.56671	−0.783355	−	0.621574i	$-0.786494\pi$
$101$	−15.7453	−1.56671	−0.783355	+	0.621574i	$0.786494\pi$
$102$	3.02715	0.299732
$103$	12.0858	1.19084	0.595422	−	0.803413i	$-0.296985\pi$
$103$	12.0858	1.19084	0.595422	+	0.803413i	$0.296985\pi$
$104$	0	0
$105$	−4.80194	−0.468621
$106$	6.91185	0.671339
$107$	−4.64071	−0.448634	−0.224317	−	0.974516i	$-0.572015\pi$
$107$	−4.64071	−0.448634	−0.224317	+	0.974516i	$0.572015\pi$
$108$	1.00000	0.0962250
$109$	−4.20344	−0.402616	−0.201308	−	0.979528i	$-0.564519\pi$
$109$	−4.20344	−0.402616	−0.201308	+	0.979528i	$0.564519\pi$
$110$	2.55496	0.243606
$111$	7.51573	0.713361
$112$	4.80194	0.453740
$113$	−0.170915	−0.0160783	−0.00803917	−	0.999968i	$-0.502559\pi$
$113$	−0.170915	−0.0160783	−0.00803917	+	0.999968i	$0.502559\pi$
$114$	3.89977	0.365247
$115$	1.64310	0.153220
$116$	5.07606	0.471301
$117$	0	0
$118$	−7.60925	−0.700488
$119$	−14.5362	−1.33253
$120$	1.00000	0.0912871
$121$	−4.47219	−0.406563
$122$	−9.65279	−0.873923
$123$	−5.89977	−0.531965
$124$	5.44504	0.488979
$125$	−1.00000	−0.0894427
$126$	−4.80194	−0.427791
$127$	5.58211	0.495332	0.247666	−	0.968846i	$-0.420336\pi$
$127$	5.58211	0.495332	0.247666	+	0.968846i	$0.420336\pi$
$128$	−1.00000	−0.0883883
$129$	−10.1468	−0.893372
$130$	0	0
$131$	−3.06100	−0.267441	−0.133720	−	0.991019i	$-0.542692\pi$
$131$	−3.06100	−0.267441	−0.133720	+	0.991019i	$0.542692\pi$
$132$	2.55496	0.222381
$133$	−18.7265	−1.62379
$134$	−0.929312	−0.0802804
$135$	−1.00000	−0.0860663
$136$	3.02715	0.259576
$137$	−1.03385	−0.0883279	−0.0441640	−	0.999024i	$-0.514062\pi$
$137$	−1.03385	−0.0883279	−0.0441640	+	0.999024i	$0.514062\pi$
$138$	1.64310	0.139870
$139$	−16.7995	−1.42492	−0.712459	−	0.701713i	$-0.752419\pi$
$139$	−16.7995	−1.42492	−0.712459	+	0.701713i	$0.752419\pi$
$140$	−4.80194	−0.405838
$141$	6.42758	0.541300
$142$	−14.9487	−1.25447
$143$	0	0
$144$	1.00000	0.0833333
$145$	−5.07606	−0.421544
$146$	−14.1129	−1.16799
$147$	16.0586	1.32449
$148$	7.51573	0.617789
$149$	17.8756	1.46443	0.732213	−	0.681075i	$-0.238487\pi$
$149$	17.8756	1.46443	0.732213	+	0.681075i	$0.238487\pi$
$150$	−1.00000	−0.0816497
$151$	0.390748	0.0317986	0.0158993	−	0.999874i	$-0.494939\pi$
$151$	0.390748	0.0317986	0.0158993	+	0.999874i	$0.494939\pi$
$152$	3.89977	0.316313
$153$	−3.02715	−0.244730
$154$	−12.2687	−0.988644
$155$	−5.44504	−0.437356
$156$	0	0
$157$	9.50902	0.758903	0.379451	−	0.925212i	$-0.376113\pi$
$157$	9.50902	0.758903	0.379451	+	0.925212i	$0.376113\pi$
$158$	5.40581	0.430063
$159$	−6.91185	−0.548146
$160$	1.00000	0.0790569
$161$	−7.89008	−0.621826
$162$	−1.00000	−0.0785674
$163$	−5.84846	−0.458087	−0.229043	−	0.973416i	$-0.573560\pi$
$163$	−5.84846	−0.458087	−0.229043	+	0.973416i	$0.573560\pi$
$164$	−5.89977	−0.460695
$165$	−2.55496	−0.198903
$166$	−4.33513	−0.336471
$167$	−2.55496	−0.197709	−0.0988543	−	0.995102i	$-0.531518\pi$
$167$	−2.55496	−0.197709	−0.0988543	+	0.995102i	$0.531518\pi$
$168$	−4.80194	−0.370478
$169$	0	0
$170$	−3.02715	−0.232172
$171$	−3.89977	−0.298223
$172$	−10.1468	−0.773683
$173$	−21.5308	−1.63696	−0.818478	−	0.574538i	$-0.805182\pi$
$173$	−21.5308	−1.63696	−0.818478	+	0.574538i	$0.805182\pi$
$174$	−5.07606	−0.384815
$175$	4.80194	0.362992
$176$	2.55496	0.192587
$177$	7.60925	0.571946
$178$	16.8267	1.26121
$179$	15.5483	1.16213	0.581066	−	0.813857i	$-0.302636\pi$
$179$	15.5483	1.16213	0.581066	+	0.813857i	$0.302636\pi$
$180$	−1.00000	−0.0745356
$181$	14.4058	1.07078	0.535388	−	0.844606i	$-0.320165\pi$
$181$	14.4058	1.07078	0.535388	+	0.844606i	$0.320165\pi$
$182$	0	0
$183$	9.65279	0.713555
$184$	1.64310	0.121131
$185$	−7.51573	−0.552567
$186$	−5.44504	−0.399250
$187$	−7.73423	−0.565583
$188$	6.42758	0.468780
$189$	4.80194	0.349290
$190$	−3.89977	−0.282919
$191$	−4.02177	−0.291005	−0.145503	−	0.989358i	$-0.546480\pi$
$191$	−4.02177	−0.291005	−0.145503	+	0.989358i	$0.546480\pi$
$192$	1.00000	0.0721688
$193$	−20.1008	−1.44689	−0.723444	−	0.690383i	$-0.757442\pi$
$193$	−20.1008	−1.44689	−0.723444	+	0.690383i	$0.757442\pi$
$194$	−17.9855	−1.29129
$195$	0	0
$196$	16.0586	1.14704
$197$	−15.3884	−1.09637	−0.548187	−	0.836356i	$-0.684682\pi$
$197$	−15.3884	−1.09637	−0.548187	+	0.836356i	$0.684682\pi$
$198$	−2.55496	−0.181573
$199$	24.7724	1.75607	0.878034	−	0.478598i	$-0.158855\pi$
$199$	24.7724	1.75607	0.878034	+	0.478598i	$0.158855\pi$
$200$	−1.00000	−0.0707107
$201$	0.929312	0.0655486
$202$	15.7453	1.10783
$203$	24.3749	1.71079
$204$	−3.02715	−0.211943
$205$	5.89977	0.412058
$206$	−12.0858	−0.842054
$207$	−1.64310	−0.114204
$208$	0	0
$209$	−9.96376	−0.689207
$210$	4.80194	0.331365
$211$	6.49396	0.447063	0.223531	−	0.974697i	$-0.428242\pi$
$211$	6.49396	0.447063	0.223531	+	0.974697i	$0.428242\pi$
$212$	−6.91185	−0.474708
$213$	14.9487	1.02427
$214$	4.64071	0.317232
$215$	10.1468	0.692003
$216$	−1.00000	−0.0680414
$217$	26.1468	1.77496
$218$	4.20344	0.284693
$219$	14.1129	0.953661
$220$	−2.55496	−0.172255
$221$	0	0
$222$	−7.51573	−0.504423
$223$	20.1250	1.34767	0.673834	−	0.738883i	$-0.264646\pi$
$223$	20.1250	1.34767	0.673834	+	0.738883i	$0.264646\pi$
$224$	−4.80194	−0.320843
$225$	1.00000	0.0666667
$226$	0.170915	0.0113691
$227$	−24.2379	−1.60872	−0.804362	−	0.594139i	$-0.797493\pi$
$227$	−24.2379	−1.60872	−0.804362	+	0.594139i	$0.797493\pi$
$228$	−3.89977	−0.258269
$229$	−2.71618	−0.179491	−0.0897453	−	0.995965i	$-0.528605\pi$
$229$	−2.71618	−0.179491	−0.0897453	+	0.995965i	$0.528605\pi$
$230$	−1.64310	−0.108343
$231$	12.2687	0.807224
$232$	−5.07606	−0.333260
$233$	−2.16421	−0.141782	−0.0708911	−	0.997484i	$-0.522584\pi$
$233$	−2.16421	−0.141782	−0.0708911	+	0.997484i	$0.522584\pi$
$234$	0	0
$235$	−6.42758	−0.419289
$236$	7.60925	0.495320
$237$	−5.40581	−0.351145
$238$	14.5362	0.942240
$239$	14.5114	0.938666	0.469333	−	0.883021i	$-0.344494\pi$
$239$	14.5114	0.938666	0.469333	+	0.883021i	$0.344494\pi$
$240$	−1.00000	−0.0645497
$241$	−18.1142	−1.16684	−0.583420	−	0.812171i	$-0.698286\pi$
$241$	−18.1142	−1.16684	−0.583420	+	0.812171i	$0.698286\pi$
$242$	4.47219	0.287483
$243$	1.00000	0.0641500
$244$	9.65279	0.617957
$245$	−16.0586	−1.02595
$246$	5.89977	0.376156
$247$	0	0
$248$	−5.44504	−0.345761
$249$	4.33513	0.274727
$250$	1.00000	0.0632456
$251$	8.55257	0.539833	0.269917	−	0.962884i	$-0.413004\pi$
$251$	8.55257	0.539833	0.269917	+	0.962884i	$0.413004\pi$
$252$	4.80194	0.302494
$253$	−4.19806	−0.263930
$254$	−5.58211	−0.350252
$255$	3.02715	0.189567
$256$	1.00000	0.0625000
$257$	1.30260	0.0812541	0.0406270	−	0.999174i	$-0.487064\pi$
$257$	1.30260	0.0812541	0.0406270	+	0.999174i	$0.487064\pi$
$258$	10.1468	0.631709
$259$	36.0901	2.24253
$260$	0	0
$261$	5.07606	0.314200
$262$	3.06100	0.189109
$263$	8.24027	0.508117	0.254059	−	0.967189i	$-0.418234\pi$
$263$	8.24027	0.508117	0.254059	+	0.967189i	$0.418234\pi$
$264$	−2.55496	−0.157247
$265$	6.91185	0.424592
$266$	18.7265	1.14819
$267$	−16.8267	−1.02978
$268$	0.929312	0.0567668
$269$	22.6601	1.38161	0.690805	−	0.723041i	$-0.257256\pi$
$269$	22.6601	1.38161	0.690805	+	0.723041i	$0.257256\pi$
$270$	1.00000	0.0608581
$271$	13.9172	0.845412	0.422706	−	0.906267i	$-0.361080\pi$
$271$	13.9172	0.845412	0.422706	+	0.906267i	$0.361080\pi$
$272$	−3.02715	−0.183548
$273$	0	0
$274$	1.03385	0.0624573
$275$	2.55496	0.154070
$276$	−1.64310	−0.0989032
$277$	−24.2610	−1.45770	−0.728851	−	0.684673i	$-0.759945\pi$
$277$	−24.2610	−1.45770	−0.728851	+	0.684673i	$0.759945\pi$
$278$	16.7995	1.00757
$279$	5.44504	0.325986
$280$	4.80194	0.286971
$281$	10.5961	0.632111	0.316055	−	0.948741i	$-0.397641\pi$
$281$	10.5961	0.632111	0.316055	+	0.948741i	$0.397641\pi$
$282$	−6.42758	−0.382757
$283$	9.86294	0.586291	0.293145	−	0.956068i	$-0.405298\pi$
$283$	9.86294	0.586291	0.293145	+	0.956068i	$0.405298\pi$
$284$	14.9487	0.887042
$285$	3.89977	0.231003
$286$	0	0
$287$	−28.3303	−1.67229
$288$	−1.00000	−0.0589256
$289$	−7.83638	−0.460964
$290$	5.07606	0.298077
$291$	17.9855	1.05433
$292$	14.1129	0.825895
$293$	5.68233	0.331965	0.165983	−	0.986129i	$-0.446920\pi$
$293$	5.68233	0.331965	0.165983	+	0.986129i	$0.446920\pi$
$294$	−16.0586	−0.936557
$295$	−7.60925	−0.443028
$296$	−7.51573	−0.436843
$297$	2.55496	0.148254
$298$	−17.8756	−1.03551
$299$	0	0
$300$	1.00000	0.0577350
$301$	−48.7241	−2.80841
$302$	−0.390748	−0.0224850
$303$	−15.7453	−0.904541
$304$	−3.89977	−0.223667
$305$	−9.65279	−0.552717
$306$	3.02715	0.173050
$307$	−11.5961	−0.661825	−0.330912	−	0.943661i	$-0.607356\pi$
$307$	−11.5961	−0.661825	−0.330912	+	0.943661i	$0.607356\pi$
$308$	12.2687	0.699077
$309$	12.0858	0.687534
$310$	5.44504	0.309258
$311$	4.43429	0.251445	0.125723	−	0.992065i	$-0.459875\pi$
$311$	4.43429	0.251445	0.125723	+	0.992065i	$0.459875\pi$
$312$	0	0
$313$	11.2881	0.638043	0.319021	−	0.947748i	$-0.396646\pi$
$313$	11.2881	0.638043	0.319021	+	0.947748i	$0.396646\pi$
$314$	−9.50902	−0.536625
$315$	−4.80194	−0.270559
$316$	−5.40581	−0.304101
$317$	−6.31229	−0.354534	−0.177267	−	0.984163i	$-0.556726\pi$
$317$	−6.31229	−0.354534	−0.177267	+	0.984163i	$0.556726\pi$
$318$	6.91185	0.387598
$319$	12.9691	0.726132
$320$	−1.00000	−0.0559017
$321$	−4.64071	−0.259019
$322$	7.89008	0.439697
$323$	11.8052	0.656858
$324$	1.00000	0.0555556
$325$	0	0
$326$	5.84846	0.323916
$327$	−4.20344	−0.232451
$328$	5.89977	0.325760
$329$	30.8649	1.70163
$330$	2.55496	0.140646
$331$	10.9554	0.602163	0.301081	−	0.953598i	$-0.402652\pi$
$331$	10.9554	0.602163	0.301081	+	0.953598i	$0.402652\pi$
$332$	4.33513	0.237921
$333$	7.51573	0.411859
$334$	2.55496	0.139801
$335$	−0.929312	−0.0507738
$336$	4.80194	0.261967
$337$	26.6668	1.45263	0.726316	−	0.687361i	$-0.241231\pi$
$337$	26.6668	1.45263	0.726316	+	0.687361i	$0.241231\pi$
$338$	0	0
$339$	−0.170915	−0.00928284
$340$	3.02715	0.164170
$341$	13.9119	0.753369
$342$	3.89977	0.210876
$343$	43.4989	2.34872
$344$	10.1468	0.547076
$345$	1.64310	0.0884618
$346$	21.5308	1.15750
$347$	25.0694	1.34579	0.672897	−	0.739736i	$-0.265050\pi$
$347$	25.0694	1.34579	0.672897	+	0.739736i	$0.265050\pi$
$348$	5.07606	0.272106
$349$	−21.5623	−1.15420	−0.577100	−	0.816673i	$-0.695816\pi$
$349$	−21.5623	−1.15420	−0.577100	+	0.816673i	$0.695816\pi$
$350$	−4.80194	−0.256674
$351$	0	0
$352$	−2.55496	−0.136180
$353$	−28.2959	−1.50604	−0.753019	−	0.657998i	$-0.771403\pi$
$353$	−28.2959	−1.50604	−0.753019	+	0.657998i	$0.771403\pi$
$354$	−7.60925	−0.404427
$355$	−14.9487	−0.793394
$356$	−16.8267	−0.891813
$357$	−14.5362	−0.769336
$358$	−15.5483	−0.821751
$359$	34.2717	1.80879	0.904396	−	0.426693i	$-0.140322\pi$
$359$	34.2717	1.80879	0.904396	+	0.426693i	$0.140322\pi$
$360$	1.00000	0.0527046
$361$	−3.79178	−0.199567
$362$	−14.4058	−0.757153
$363$	−4.47219	−0.234729
$364$	0	0
$365$	−14.1129	−0.738703
$366$	−9.65279	−0.504560
$367$	−23.4209	−1.22256	−0.611280	−	0.791414i	$-0.709345\pi$
$367$	−23.4209	−1.22256	−0.611280	+	0.791414i	$0.709345\pi$
$368$	−1.64310	−0.0856527
$369$	−5.89977	−0.307130
$370$	7.51573	0.390724
$371$	−33.1903	−1.72315
$372$	5.44504	0.282312
$373$	1.82371	0.0944280	0.0472140	−	0.998885i	$-0.484966\pi$
$373$	1.82371	0.0944280	0.0472140	+	0.998885i	$0.484966\pi$
$374$	7.73423	0.399928
$375$	−1.00000	−0.0516398
$376$	−6.42758	−0.331477
$377$	0	0
$378$	−4.80194	−0.246985
$379$	−15.3260	−0.787245	−0.393623	−	0.919272i	$-0.628778\pi$
$379$	−15.3260	−0.787245	−0.393623	+	0.919272i	$0.628778\pi$
$380$	3.89977	0.200054
$381$	5.58211	0.285980
$382$	4.02177	0.205772
$383$	−29.6722	−1.51618	−0.758089	−	0.652152i	$-0.773867\pi$
$383$	−29.6722	−1.51618	−0.758089	+	0.652152i	$0.773867\pi$
$384$	−1.00000	−0.0510310
$385$	−12.2687	−0.625273
$386$	20.1008	1.02310
$387$	−10.1468	−0.515788
$388$	17.9855	0.913077
$389$	11.8291	0.599758	0.299879	−	0.953977i	$-0.403054\pi$
$389$	11.8291	0.599758	0.299879	+	0.953977i	$0.403054\pi$
$390$	0	0
$391$	4.97392	0.251542
$392$	−16.0586	−0.811082
$393$	−3.06100	−0.154407
$394$	15.3884	0.775254
$395$	5.40581	0.271996
$396$	2.55496	0.128391
$397$	12.1153	0.608049	0.304025	−	0.952664i	$-0.401670\pi$
$397$	12.1153	0.608049	0.304025	+	0.952664i	$0.401670\pi$
$398$	−24.7724	−1.24173
$399$	−18.7265	−0.937496
$400$	1.00000	0.0500000
$401$	−10.8291	−0.540779	−0.270389	−	0.962751i	$-0.587152\pi$
$401$	−10.8291	−0.540779	−0.270389	+	0.962751i	$0.587152\pi$
$402$	−0.929312	−0.0463499
$403$	0	0
$404$	−15.7453	−0.783355
$405$	−1.00000	−0.0496904
$406$	−24.3749	−1.20971
$407$	19.2024	0.951826
$408$	3.02715	0.149866
$409$	−33.9396	−1.67820	−0.839102	−	0.543973i	$-0.816919\pi$
$409$	−33.9396	−1.67820	−0.839102	+	0.543973i	$0.816919\pi$
$410$	−5.89977	−0.291369
$411$	−1.03385	−0.0509962
$412$	12.0858	0.595422
$413$	36.5392	1.79797
$414$	1.64310	0.0807542
$415$	−4.33513	−0.212803
$416$	0	0
$417$	−16.7995	−0.822677
$418$	9.96376	0.487343
$419$	26.8562	1.31201	0.656006	−	0.754755i	$-0.272244\pi$
$419$	26.8562	1.31201	0.656006	+	0.754755i	$0.272244\pi$
$420$	−4.80194	−0.234311
$421$	27.9928	1.36429	0.682143	−	0.731219i	$-0.261048\pi$
$421$	27.9928	1.36429	0.682143	+	0.731219i	$0.261048\pi$
$422$	−6.49396	−0.316121
$423$	6.42758	0.312520
$424$	6.91185	0.335669
$425$	−3.02715	−0.146838
$426$	−14.9487	−0.724266
$427$	46.3521	2.24314
$428$	−4.64071	−0.224317
$429$	0	0
$430$	−10.1468	−0.489320
$431$	−33.4088	−1.60925	−0.804623	−	0.593787i	$-0.797632\pi$
$431$	−33.4088	−1.60925	−0.804623	+	0.593787i	$0.797632\pi$
$432$	1.00000	0.0481125
$433$	−13.6420	−0.655595	−0.327797	−	0.944748i	$-0.606306\pi$
$433$	−13.6420	−0.655595	−0.327797	+	0.944748i	$0.606306\pi$
$434$	−26.1468	−1.25508
$435$	−5.07606	−0.243379
$436$	−4.20344	−0.201308
$437$	6.40773	0.306523
$438$	−14.1129	−0.674340
$439$	−30.6437	−1.46254	−0.731272	−	0.682086i	$-0.761073\pi$
$439$	−30.6437	−1.46254	−0.731272	+	0.682086i	$0.761073\pi$
$440$	2.55496	0.121803
$441$	16.0586	0.764696
$442$	0	0
$443$	−19.7409	−0.937920	−0.468960	−	0.883219i	$-0.655371\pi$
$443$	−19.7409	−0.937920	−0.468960	+	0.883219i	$0.655371\pi$
$444$	7.51573	0.356681
$445$	16.8267	0.797662
$446$	−20.1250	−0.952946
$447$	17.8756	0.845487
$448$	4.80194	0.226870
$449$	36.2664	1.71152	0.855758	−	0.517377i	$-0.173091\pi$
$449$	36.2664	1.71152	0.855758	+	0.517377i	$0.173091\pi$
$450$	−1.00000	−0.0471405
$451$	−15.0737	−0.709791
$452$	−0.170915	−0.00803917
$453$	0.390748	0.0183589
$454$	24.2379	1.13754
$455$	0	0
$456$	3.89977	0.182624
$457$	3.55602	0.166344	0.0831719	−	0.996535i	$-0.473495\pi$
$457$	3.55602	0.166344	0.0831719	+	0.996535i	$0.473495\pi$
$458$	2.71618	0.126919
$459$	−3.02715	−0.141295
$460$	1.64310	0.0766101
$461$	1.46011	0.0680040	0.0340020	−	0.999422i	$-0.489175\pi$
$461$	1.46011	0.0680040	0.0340020	+	0.999422i	$0.489175\pi$
$462$	−12.2687	−0.570794
$463$	−13.7942	−0.641069	−0.320535	−	0.947237i	$-0.603863\pi$
$463$	−13.7942	−0.641069	−0.320535	+	0.947237i	$0.603863\pi$
$464$	5.07606	0.235650
$465$	−5.44504	−0.252508
$466$	2.16421	0.100255
$467$	−1.72886	−0.0800020	−0.0400010	−	0.999200i	$-0.512736\pi$
$467$	−1.72886	−0.0800020	−0.0400010	+	0.999200i	$0.512736\pi$
$468$	0	0
$469$	4.46250	0.206059
$470$	6.42758	0.296482
$471$	9.50902	0.438153
$472$	−7.60925	−0.350244
$473$	−25.9245	−1.19201
$474$	5.40581	0.248297
$475$	−3.89977	−0.178934
$476$	−14.5362	−0.666264
$477$	−6.91185	−0.316472
$478$	−14.5114	−0.663737
$479$	14.5496	0.664787	0.332394	−	0.943141i	$-0.392144\pi$
$479$	14.5496	0.664787	0.332394	+	0.943141i	$0.392144\pi$
$480$	1.00000	0.0456435
$481$	0	0
$482$	18.1142	0.825080
$483$	−7.89008	−0.359011
$484$	−4.47219	−0.203281
$485$	−17.9855	−0.816681
$486$	−1.00000	−0.0453609
$487$	30.5526	1.38447	0.692234	−	0.721673i	$-0.256626\pi$
$487$	30.5526	1.38447	0.692234	+	0.721673i	$0.256626\pi$
$488$	−9.65279	−0.436961
$489$	−5.84846	−0.264477
$490$	16.0586	0.725454
$491$	9.68233	0.436958	0.218479	−	0.975842i	$-0.429891\pi$
$491$	9.68233	0.436958	0.218479	+	0.975842i	$0.429891\pi$
$492$	−5.89977	−0.265982
$493$	−15.3660	−0.692050
$494$	0	0
$495$	−2.55496	−0.114837
$496$	5.44504	0.244490
$497$	71.7827	3.21989
$498$	−4.33513	−0.194262
$499$	18.6025	0.832764	0.416382	−	0.909190i	$-0.363298\pi$
$499$	18.6025	0.832764	0.416382	+	0.909190i	$0.363298\pi$
$500$	−1.00000	−0.0447214
$501$	−2.55496	−0.114147
$502$	−8.55257	−0.381720
$503$	41.6644	1.85772	0.928862	−	0.370426i	$-0.120788\pi$
$503$	41.6644	1.85772	0.928862	+	0.370426i	$0.120788\pi$
$504$	−4.80194	−0.213895
$505$	15.7453	0.700654
$506$	4.19806	0.186627
$507$	0	0
$508$	5.58211	0.247666
$509$	41.1648	1.82460	0.912299	−	0.409525i	$-0.134306\pi$
$509$	41.1648	1.82460	0.912299	+	0.409525i	$0.134306\pi$
$510$	−3.02715	−0.134044
$511$	67.7693	2.99794
$512$	−1.00000	−0.0441942
$513$	−3.89977	−0.172179
$514$	−1.30260	−0.0574553
$515$	−12.0858	−0.532562
$516$	−10.1468	−0.446686
$517$	16.4222	0.722248
$518$	−36.0901	−1.58571
$519$	−21.5308	−0.945097
$520$	0	0
$521$	1.12737	0.0493912	0.0246956	−	0.999695i	$-0.492138\pi$
$521$	1.12737	0.0493912	0.0246956	+	0.999695i	$0.492138\pi$
$522$	−5.07606	−0.222173
$523$	−22.7922	−0.996635	−0.498318	−	0.866994i	$-0.666049\pi$
$523$	−22.7922	−0.996635	−0.498318	+	0.866994i	$0.666049\pi$
$524$	−3.06100	−0.133720
$525$	4.80194	0.209574
$526$	−8.24027	−0.359293
$527$	−16.4829	−0.718008
$528$	2.55496	0.111190
$529$	−20.3002	−0.882618
$530$	−6.91185	−0.300232
$531$	7.60925	0.330213
$532$	−18.7265	−0.811895
$533$	0	0
$534$	16.8267	0.728162
$535$	4.64071	0.200635
$536$	−0.929312	−0.0401402
$537$	15.5483	0.670957
$538$	−22.6601	−0.976946
$539$	41.0291	1.76725
$540$	−1.00000	−0.0430331
$541$	−41.1148	−1.76766	−0.883832	−	0.467804i	$-0.845045\pi$
$541$	−41.1148	−1.76766	−0.883832	+	0.467804i	$0.845045\pi$
$542$	−13.9172	−0.597796
$543$	14.4058	0.618213
$544$	3.02715	0.129788
$545$	4.20344	0.180056
$546$	0	0
$547$	3.96615	0.169580	0.0847901	−	0.996399i	$-0.472978\pi$
$547$	3.96615	0.169580	0.0847901	+	0.996399i	$0.472978\pi$
$548$	−1.03385	−0.0441640
$549$	9.65279	0.411971
$550$	−2.55496	−0.108944
$551$	−19.7955	−0.843316
$552$	1.64310	0.0699352
$553$	−25.9584	−1.10386
$554$	24.2610	1.03075
$555$	−7.51573	−0.319025
$556$	−16.7995	−0.712459
$557$	−4.25236	−0.180178	−0.0900891	−	0.995934i	$-0.528715\pi$
$557$	−4.25236	−0.180178	−0.0900891	+	0.995934i	$0.528715\pi$
$558$	−5.44504	−0.230507
$559$	0	0
$560$	−4.80194	−0.202919
$561$	−7.73423	−0.326540
$562$	−10.5961	−0.446970
$563$	−32.7700	−1.38109	−0.690546	−	0.723289i	$-0.742629\pi$
$563$	−32.7700	−1.38109	−0.690546	+	0.723289i	$0.742629\pi$
$564$	6.42758	0.270650
$565$	0.170915	0.00719046
$566$	−9.86294	−0.414570
$567$	4.80194	0.201662
$568$	−14.9487	−0.627233
$569$	−20.6189	−0.864391	−0.432195	−	0.901780i	$-0.642261\pi$
$569$	−20.6189	−0.864391	−0.432195	+	0.901780i	$0.642261\pi$
$570$	−3.89977	−0.163343
$571$	23.1215	0.967606	0.483803	−	0.875177i	$-0.339255\pi$
$571$	23.1215	0.967606	0.483803	+	0.875177i	$0.339255\pi$
$572$	0	0
$573$	−4.02177	−0.168012
$574$	28.3303	1.18249
$575$	−1.64310	−0.0685222
$576$	1.00000	0.0416667
$577$	28.0000	1.16566	0.582828	−	0.812596i	$-0.301946\pi$
$577$	28.0000	1.16566	0.582828	+	0.812596i	$0.301946\pi$
$578$	7.83638	0.325950
$579$	−20.1008	−0.835362
$580$	−5.07606	−0.210772
$581$	20.8170	0.863635
$582$	−17.9855	−0.745524
$583$	−17.6595	−0.731382
$584$	−14.1129	−0.583996
$585$	0	0
$586$	−5.68233	−0.234735
$587$	21.1081	0.871225	0.435613	−	0.900134i	$-0.356532\pi$
$587$	21.1081	0.871225	0.435613	+	0.900134i	$0.356532\pi$
$588$	16.0586	0.662246
$589$	−21.2344	−0.874949
$590$	7.60925	0.313268
$591$	−15.3884	−0.632992
$592$	7.51573	0.308895
$593$	−15.4276	−0.633535	−0.316767	−	0.948503i	$-0.602597\pi$
$593$	−15.4276	−0.633535	−0.316767	+	0.948503i	$0.602597\pi$
$594$	−2.55496	−0.104831
$595$	14.5362	0.595925
$596$	17.8756	0.732213
$597$	24.7724	1.01387
$598$	0	0
$599$	9.16985	0.374670	0.187335	−	0.982296i	$-0.440015\pi$
$599$	9.16985	0.374670	0.187335	+	0.982296i	$0.440015\pi$
$600$	−1.00000	−0.0408248
$601$	−25.8864	−1.05593	−0.527963	−	0.849267i	$-0.677044\pi$
$601$	−25.8864	−1.05593	−0.527963	+	0.849267i	$0.677044\pi$
$602$	48.7241	1.98584
$603$	0.929312	0.0378445
$604$	0.390748	0.0158993
$605$	4.47219	0.181820
$606$	15.7453	0.639607
$607$	−11.6093	−0.471205	−0.235603	−	0.971850i	$-0.575706\pi$
$607$	−11.6093	−0.471205	−0.235603	+	0.971850i	$0.575706\pi$
$608$	3.89977	0.158157
$609$	24.3749	0.987723
$610$	9.65279	0.390830
$611$	0	0
$612$	−3.02715	−0.122365
$613$	16.5985	0.670407	0.335204	−	0.942146i	$-0.391195\pi$
$613$	16.5985	0.670407	0.335204	+	0.942146i	$0.391195\pi$
$614$	11.5961	0.467981
$615$	5.89977	0.237902
$616$	−12.2687	−0.494322
$617$	−33.4373	−1.34613	−0.673067	−	0.739582i	$-0.735023\pi$
$617$	−33.4373	−1.34613	−0.673067	+	0.739582i	$0.735023\pi$
$618$	−12.0858	−0.486160
$619$	25.4198	1.02171	0.510854	−	0.859667i	$-0.329329\pi$
$619$	25.4198	1.02171	0.510854	+	0.859667i	$0.329329\pi$
$620$	−5.44504	−0.218678
$621$	−1.64310	−0.0659355
$622$	−4.43429	−0.177799
$623$	−80.8007	−3.23721
$624$	0	0
$625$	1.00000	0.0400000
$626$	−11.2881	−0.451164
$627$	−9.96376	−0.397914
$628$	9.50902	0.379451
$629$	−22.7512	−0.907150
$630$	4.80194	0.191314
$631$	15.1879	0.604621	0.302310	−	0.953210i	$-0.402242\pi$
$631$	15.1879	0.604621	0.302310	+	0.953210i	$0.402242\pi$
$632$	5.40581	0.215032
$633$	6.49396	0.258112
$634$	6.31229	0.250693
$635$	−5.58211	−0.221519
$636$	−6.91185	−0.274073
$637$	0	0
$638$	−12.9691	−0.513453
$639$	14.9487	0.591361
$640$	1.00000	0.0395285
$641$	16.8009	0.663595	0.331797	−	0.943351i	$-0.392345\pi$
$641$	16.8009	0.663595	0.331797	+	0.943351i	$0.392345\pi$
$642$	4.64071	0.183154
$643$	−35.2597	−1.39050	−0.695252	−	0.718766i	$-0.744707\pi$
$643$	−35.2597	−1.39050	−0.695252	+	0.718766i	$0.744707\pi$
$644$	−7.89008	−0.310913
$645$	10.1468	0.399528
$646$	−11.8052	−0.464469
$647$	−26.7985	−1.05356	−0.526778	−	0.850003i	$-0.676600\pi$
$647$	−26.7985	−1.05356	−0.526778	+	0.850003i	$0.676600\pi$
$648$	−1.00000	−0.0392837
$649$	19.4413	0.763139
$650$	0	0
$651$	26.1468	1.02477
$652$	−5.84846	−0.229043
$653$	−10.8358	−0.424037	−0.212019	−	0.977266i	$-0.568004\pi$
$653$	−10.8358	−0.424037	−0.212019	+	0.977266i	$0.568004\pi$
$654$	4.20344	0.164367
$655$	3.06100	0.119603
$656$	−5.89977	−0.230347
$657$	14.1129	0.550597
$658$	−30.8649	−1.20324
$659$	49.3870	1.92385	0.961923	−	0.273322i	$-0.0881223\pi$
$659$	49.3870	1.92385	0.961923	+	0.273322i	$0.0881223\pi$
$660$	−2.55496	−0.0994516
$661$	2.18167	0.0848571	0.0424285	−	0.999100i	$-0.486491\pi$
$661$	2.18167	0.0848571	0.0424285	+	0.999100i	$0.486491\pi$
$662$	−10.9554	−0.425793
$663$	0	0
$664$	−4.33513	−0.168236
$665$	18.7265	0.726181
$666$	−7.51573	−0.291229
$667$	−8.34050	−0.322946
$668$	−2.55496	−0.0988543
$669$	20.1250	0.778077
$670$	0.929312	0.0359025
$671$	24.6625	0.952085
$672$	−4.80194	−0.185239
$673$	−24.2319	−0.934072	−0.467036	−	0.884238i	$-0.654678\pi$
$673$	−24.2319	−0.934072	−0.467036	+	0.884238i	$0.654678\pi$
$674$	−26.6668	−1.02717
$675$	1.00000	0.0384900
$676$	0	0
$677$	24.0422	0.924017	0.462009	−	0.886875i	$-0.347129\pi$
$677$	24.0422	0.924017	0.462009	+	0.886875i	$0.347129\pi$
$678$	0.170915	0.00656396
$679$	86.3654	3.31440
$680$	−3.02715	−0.116086
$681$	−24.2379	−0.928798
$682$	−13.9119	−0.532712
$683$	−24.3183	−0.930512	−0.465256	−	0.885176i	$-0.654038\pi$
$683$	−24.3183	−0.930512	−0.465256	+	0.885176i	$0.654038\pi$
$684$	−3.89977	−0.149112
$685$	1.03385	0.0395014
$686$	−43.4989	−1.66079
$687$	−2.71618	−0.103629
$688$	−10.1468	−0.386841
$689$	0	0
$690$	−1.64310	−0.0625519
$691$	18.2054	0.692564	0.346282	−	0.938130i	$-0.387444\pi$
$691$	18.2054	0.692564	0.346282	+	0.938130i	$0.387444\pi$
$692$	−21.5308	−0.818478
$693$	12.2687	0.466051
$694$	−25.0694	−0.951620
$695$	16.7995	0.637243
$696$	−5.07606	−0.192408
$697$	17.8595	0.676476
$698$	21.5623	0.816143
$699$	−2.16421	−0.0818580
$700$	4.80194	0.181496
$701$	−16.0441	−0.605978	−0.302989	−	0.952994i	$-0.597985\pi$
$701$	−16.0441	−0.605978	−0.302989	+	0.952994i	$0.597985\pi$
$702$	0	0
$703$	−29.3096	−1.10543
$704$	2.55496	0.0962936
$705$	−6.42758	−0.242077
$706$	28.2959	1.06493
$707$	−75.6077	−2.84352
$708$	7.60925	0.285973
$709$	−20.8025	−0.781255	−0.390628	−	0.920549i	$-0.627742\pi$
$709$	−20.8025	−0.781255	−0.390628	+	0.920549i	$0.627742\pi$
$710$	14.9487	0.561014
$711$	−5.40581	−0.202734
$712$	16.8267	0.630607
$713$	−8.94677	−0.335059
$714$	14.5362	0.544003
$715$	0	0
$716$	15.5483	0.581066
$717$	14.5114	0.541939
$718$	−34.2717	−1.27901
$719$	−40.3424	−1.50452	−0.752259	−	0.658867i	$-0.771036\pi$
$719$	−40.3424	−1.50452	−0.752259	+	0.658867i	$0.771036\pi$
$720$	−1.00000	−0.0372678
$721$	58.0350	2.16134
$722$	3.79178	0.141115
$723$	−18.1142	−0.673675
$724$	14.4058	0.535388
$725$	5.07606	0.188520
$726$	4.47219	0.165978
$727$	−47.2073	−1.75082	−0.875410	−	0.483380i	$-0.839409\pi$
$727$	−47.2073	−1.75082	−0.875410	+	0.483380i	$0.839409\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	14.1129	0.522342
$731$	30.7157	1.13606
$732$	9.65279	0.356777
$733$	41.5424	1.53440	0.767202	−	0.641406i	$-0.221648\pi$
$733$	41.5424	1.53440	0.767202	+	0.641406i	$0.221648\pi$
$734$	23.4209	0.864480
$735$	−16.0586	−0.592331
$736$	1.64310	0.0605656
$737$	2.37435	0.0874605
$738$	5.89977	0.217174
$739$	26.3811	0.970443	0.485221	−	0.874391i	$-0.338739\pi$
$739$	26.3811	0.970443	0.485221	+	0.874391i	$0.338739\pi$
$740$	−7.51573	−0.276284
$741$	0	0
$742$	33.1903	1.21845
$743$	−20.2881	−0.744299	−0.372150	−	0.928173i	$-0.621379\pi$
$743$	−20.2881	−0.744299	−0.372150	+	0.928173i	$0.621379\pi$
$744$	−5.44504	−0.199625
$745$	−17.8756	−0.654912
$746$	−1.82371	−0.0667707
$747$	4.33513	0.158614
$748$	−7.73423	−0.282792
$749$	−22.2844	−0.814254
$750$	1.00000	0.0365148
$751$	−21.1280	−0.770970	−0.385485	−	0.922714i	$-0.625966\pi$
$751$	−21.1280	−0.770970	−0.385485	+	0.922714i	$0.625966\pi$
$752$	6.42758	0.234390
$753$	8.55257	0.311673
$754$	0	0
$755$	−0.390748	−0.0142208
$756$	4.80194	0.174645
$757$	−17.3274	−0.629773	−0.314887	−	0.949129i	$-0.601967\pi$
$757$	−17.3274	−0.629773	−0.314887	+	0.949129i	$0.601967\pi$
$758$	15.3260	0.556666
$759$	−4.19806	−0.152380
$760$	−3.89977	−0.141460
$761$	35.4282	1.28427	0.642135	−	0.766591i	$-0.278049\pi$
$761$	35.4282	1.28427	0.642135	+	0.766591i	$0.278049\pi$
$762$	−5.58211	−0.202218
$763$	−20.1847	−0.730733
$764$	−4.02177	−0.145503
$765$	3.02715	0.109447
$766$	29.6722	1.07210
$767$	0	0
$768$	1.00000	0.0360844
$769$	49.5062	1.78524	0.892619	−	0.450812i	$-0.148866\pi$
$769$	49.5062	1.78524	0.892619	+	0.450812i	$0.148866\pi$
$770$	12.2687	0.442135
$771$	1.30260	0.0469121
$772$	−20.1008	−0.723444
$773$	27.9235	1.00434	0.502169	−	0.864770i	$-0.332536\pi$
$773$	27.9235	1.00434	0.502169	+	0.864770i	$0.332536\pi$
$774$	10.1468	0.364717
$775$	5.44504	0.195592
$776$	−17.9855	−0.645643
$777$	36.0901	1.29472
$778$	−11.8291	−0.424093
$779$	23.0078	0.824339
$780$	0	0
$781$	38.1933	1.36666
$782$	−4.97392	−0.177867
$783$	5.07606	0.181404
$784$	16.0586	0.573522
$785$	−9.50902	−0.339392
$786$	3.06100	0.109182
$787$	28.7778	1.02582	0.512908	−	0.858443i	$-0.328568\pi$
$787$	28.7778	1.02582	0.512908	+	0.858443i	$0.328568\pi$
$788$	−15.3884	−0.548187
$789$	8.24027	0.293362
$790$	−5.40581	−0.192330
$791$	−0.820724	−0.0291816
$792$	−2.55496	−0.0907865
$793$	0	0
$794$	−12.1153	−0.429956
$795$	6.91185	0.245138
$796$	24.7724	0.878034
$797$	−14.6752	−0.519821	−0.259910	−	0.965633i	$-0.583693\pi$
$797$	−14.6752	−0.519821	−0.259910	+	0.965633i	$0.583693\pi$
$798$	18.7265	0.662910
$799$	−19.4572	−0.688348
$800$	−1.00000	−0.0353553
$801$	−16.8267	−0.594542
$802$	10.8291	0.382388
$803$	36.0579	1.27245
$804$	0.929312	0.0327743
$805$	7.89008	0.278089
$806$	0	0
$807$	22.6601	0.797673
$808$	15.7453	0.553916
$809$	−25.4946	−0.896341	−0.448170	−	0.893948i	$-0.647924\pi$
$809$	−25.4946	−0.896341	−0.448170	+	0.893948i	$0.647924\pi$
$810$	1.00000	0.0351364
$811$	−8.99867	−0.315986	−0.157993	−	0.987440i	$-0.550502\pi$
$811$	−8.99867	−0.315986	−0.157993	+	0.987440i	$0.550502\pi$
$812$	24.3749	0.855393
$813$	13.9172	0.488099
$814$	−19.2024	−0.673043
$815$	5.84846	0.204863
$816$	−3.02715	−0.105971
$817$	39.5700	1.38438
$818$	33.9396	1.18667
$819$	0	0
$820$	5.89977	0.206029
$821$	−37.1105	−1.29517	−0.647583	−	0.761995i	$-0.724220\pi$
$821$	−37.1105	−1.29517	−0.647583	+	0.761995i	$0.724220\pi$
$822$	1.03385	0.0360597
$823$	−11.1903	−0.390069	−0.195035	−	0.980796i	$-0.562482\pi$
$823$	−11.1903	−0.390069	−0.195035	+	0.980796i	$0.562482\pi$
$824$	−12.0858	−0.421027
$825$	2.55496	0.0889522
$826$	−36.5392	−1.27136
$827$	−27.7808	−0.966032	−0.483016	−	0.875612i	$-0.660459\pi$
$827$	−27.7808	−0.966032	−0.483016	+	0.875612i	$0.660459\pi$
$828$	−1.64310	−0.0571018
$829$	−26.5633	−0.922582	−0.461291	−	0.887249i	$-0.652614\pi$
$829$	−26.5633	−0.922582	−0.461291	+	0.887249i	$0.652614\pi$
$830$	4.33513	0.150474
$831$	−24.2610	−0.841604
$832$	0	0
$833$	−48.6118	−1.68430
$834$	16.7995	0.581721
$835$	2.55496	0.0884180
$836$	−9.96376	−0.344604
$837$	5.44504	0.188208
$838$	−26.8562	−0.927733
$839$	−3.92884	−0.135639	−0.0678193	−	0.997698i	$-0.521604\pi$
$839$	−3.92884	−0.135639	−0.0678193	+	0.997698i	$0.521604\pi$
$840$	4.80194	0.165683
$841$	−3.23357	−0.111502
$842$	−27.9928	−0.964696
$843$	10.5961	0.364949
$844$	6.49396	0.223531
$845$	0	0
$846$	−6.42758	−0.220985
$847$	−21.4752	−0.737896
$848$	−6.91185	−0.237354
$849$	9.86294	0.338495
$850$	3.02715	0.103830
$851$	−12.3491	−0.423323
$852$	14.9487	0.512134
$853$	−48.2097	−1.65067	−0.825334	−	0.564645i	$-0.809013\pi$
$853$	−48.2097	−1.65067	−0.825334	+	0.564645i	$0.809013\pi$
$854$	−46.3521	−1.58614
$855$	3.89977	0.133369
$856$	4.64071	0.158616
$857$	41.2976	1.41070	0.705349	−	0.708860i	$-0.250790\pi$
$857$	41.2976	1.41070	0.705349	+	0.708860i	$0.250790\pi$
$858$	0	0
$859$	−42.1041	−1.43657	−0.718286	−	0.695748i	$-0.755073\pi$
$859$	−42.1041	−1.43657	−0.718286	+	0.695748i	$0.755073\pi$
$860$	10.1468	0.346001
$861$	−28.3303	−0.965495
$862$	33.4088	1.13791
$863$	45.0646	1.53402	0.767008	−	0.641638i	$-0.221745\pi$
$863$	45.0646	1.53402	0.767008	+	0.641638i	$0.221745\pi$
$864$	−1.00000	−0.0340207
$865$	21.5308	0.732069
$866$	13.6420	0.463575
$867$	−7.83638	−0.266137
$868$	26.1468	0.887479
$869$	−13.8116	−0.468527
$870$	5.07606	0.172095
$871$	0	0
$872$	4.20344	0.142346
$873$	17.9855	0.608718
$874$	−6.40773	−0.216745
$875$	−4.80194	−0.162335
$876$	14.1129	0.476831
$877$	−33.4935	−1.13099	−0.565497	−	0.824750i	$-0.691316\pi$
$877$	−33.4935	−1.13099	−0.565497	+	0.824750i	$0.691316\pi$
$878$	30.6437	1.03417
$879$	5.68233	0.191660
$880$	−2.55496	−0.0861276
$881$	46.0431	1.55123	0.775615	−	0.631206i	$-0.217440\pi$
$881$	46.0431	1.55123	0.775615	+	0.631206i	$0.217440\pi$
$882$	−16.0586	−0.540721
$883$	−41.8629	−1.40880	−0.704400	−	0.709803i	$-0.748784\pi$
$883$	−41.8629	−1.40880	−0.704400	+	0.709803i	$0.748784\pi$
$884$	0	0
$885$	−7.60925	−0.255782
$886$	19.7409	0.663210
$887$	23.8866	0.802034	0.401017	−	0.916071i	$-0.368657\pi$
$887$	23.8866	0.802034	0.401017	+	0.916071i	$0.368657\pi$
$888$	−7.51573	−0.252211
$889$	26.8049	0.899008
$890$	−16.8267	−0.564032
$891$	2.55496	0.0855943
$892$	20.1250	0.673834
$893$	−25.0661	−0.838805
$894$	−17.8756	−0.597850
$895$	−15.5483	−0.519721
$896$	−4.80194	−0.160421
$897$	0	0
$898$	−36.2664	−1.21022
$899$	27.6394	0.921825
$900$	1.00000	0.0333333
$901$	20.9232	0.697053
$902$	15.0737	0.501898
$903$	−48.7241	−1.62144
$904$	0.170915	0.00568455
$905$	−14.4058	−0.478865
$906$	−0.390748	−0.0129817
$907$	−20.4136	−0.677822	−0.338911	−	0.940818i	$-0.610059\pi$
$907$	−20.4136	−0.677822	−0.338911	+	0.940818i	$0.610059\pi$
$908$	−24.2379	−0.804362
$909$	−15.7453	−0.522237
$910$	0	0
$911$	23.0108	0.762380	0.381190	−	0.924497i	$-0.375514\pi$
$911$	23.0108	0.762380	0.381190	+	0.924497i	$0.375514\pi$
$912$	−3.89977	−0.129134
$913$	11.0761	0.366564
$914$	−3.55602	−0.117623
$915$	−9.65279	−0.319111
$916$	−2.71618	−0.0897453
$917$	−14.6987	−0.485395
$918$	3.02715	0.0999107
$919$	−38.3327	−1.26448	−0.632240	−	0.774773i	$-0.717864\pi$
$919$	−38.3327	−1.26448	−0.632240	+	0.774773i	$0.717864\pi$
$920$	−1.64310	−0.0541715
$921$	−11.5961	−0.382105
$922$	−1.46011	−0.0480861
$923$	0	0
$924$	12.2687	0.403612
$925$	7.51573	0.247116
$926$	13.7942	0.453304
$927$	12.0858	0.396948
$928$	−5.07606	−0.166630
$929$	15.3515	0.503667	0.251834	−	0.967771i	$-0.418966\pi$
$929$	15.3515	0.503667	0.251834	+	0.967771i	$0.418966\pi$
$930$	5.44504	0.178550
$931$	−62.6249	−2.05245
$932$	−2.16421	−0.0708911
$933$	4.43429	0.145172
$934$	1.72886	0.0565699
$935$	7.73423	0.252936
$936$	0	0
$937$	51.3629	1.67795	0.838976	−	0.544169i	$-0.183155\pi$
$937$	51.3629	1.67795	0.838976	+	0.544169i	$0.183155\pi$
$938$	−4.46250	−0.145706
$939$	11.2881	0.368374
$940$	−6.42758	−0.209645
$941$	−17.2413	−0.562052	−0.281026	−	0.959700i	$-0.590675\pi$
$941$	−17.2413	−0.562052	−0.281026	+	0.959700i	$0.590675\pi$
$942$	−9.50902	−0.309821
$943$	9.69394	0.315678
$944$	7.60925	0.247660
$945$	−4.80194	−0.156207
$946$	25.9245	0.842879
$947$	5.54586	0.180216	0.0901081	−	0.995932i	$-0.471279\pi$
$947$	5.54586	0.180216	0.0901081	+	0.995932i	$0.471279\pi$
$948$	−5.40581	−0.175573
$949$	0	0
$950$	3.89977	0.126525
$951$	−6.31229	−0.204690
$952$	14.5362	0.471120
$953$	−50.1584	−1.62479	−0.812394	−	0.583108i	$-0.801836\pi$
$953$	−50.1584	−1.62479	−0.812394	+	0.583108i	$0.801836\pi$
$954$	6.91185	0.223780
$955$	4.02177	0.130141
$956$	14.5114	0.469333
$957$	12.9691	0.419233
$958$	−14.5496	−0.470076
$959$	−4.96449	−0.160312
$960$	−1.00000	−0.0322749
$961$	−1.35152	−0.0435974
$962$	0	0
$963$	−4.64071	−0.149545
$964$	−18.1142	−0.583420
$965$	20.1008	0.647068
$966$	7.89008	0.253859
$967$	−13.6890	−0.440210	−0.220105	−	0.975476i	$-0.570640\pi$
$967$	−13.6890	−0.440210	−0.220105	+	0.975476i	$0.570640\pi$
$968$	4.47219	0.143742
$969$	11.8052	0.379237
$970$	17.9855	0.577480
$971$	−50.6075	−1.62407	−0.812035	−	0.583608i	$-0.801640\pi$
$971$	−50.6075	−1.62407	−0.812035	+	0.583608i	$0.801640\pi$
$972$	1.00000	0.0320750
$973$	−80.6704	−2.58617
$974$	−30.5526	−0.978967
$975$	0	0
$976$	9.65279	0.308978
$977$	−11.2959	−0.361388	−0.180694	−	0.983539i	$-0.557834\pi$
$977$	−11.2959	−0.361388	−0.180694	+	0.983539i	$0.557834\pi$
$978$	5.84846	0.187013
$979$	−42.9915	−1.37401
$980$	−16.0586	−0.512973
$981$	−4.20344	−0.134205
$982$	−9.68233	−0.308976
$983$	−36.8194	−1.17436	−0.587178	−	0.809458i	$-0.699761\pi$
$983$	−36.8194	−1.17436	−0.587178	+	0.809458i	$0.699761\pi$
$984$	5.89977	0.188078
$985$	15.3884	0.490314
$986$	15.3660	0.489353
$987$	30.8649	0.982439
$988$	0	0
$989$	16.6722	0.530144
$990$	2.55496	0.0812019
$991$	10.8254	0.343879	0.171940	−	0.985108i	$-0.444997\pi$
$991$	10.8254	0.343879	0.171940	+	0.985108i	$0.444997\pi$
$992$	−5.44504	−0.172880
$993$	10.9554	0.347659
$994$	−71.7827	−2.27681
$995$	−24.7724	−0.785338
$996$	4.33513	0.137364
$997$	−4.30319	−0.136283	−0.0681417	−	0.997676i	$-0.521707\pi$
$997$	−4.30319	−0.136283	−0.0681417	+	0.997676i	$0.521707\pi$
$998$	−18.6025	−0.588853
$999$	7.51573	0.237787

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5070.2.a.bo.1.3	✓	3
13.5	odd	4		5070.2.b.w.1351.6		6
13.8	odd	4		5070.2.b.w.1351.1		6
13.12	even	2		5070.2.a.bx.1.1	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5070.2.a.bo.1.3	✓	3	1.1	even	1	trivial
5070.2.a.bx.1.1	yes	3	13.12	even	2
5070.2.b.w.1351.1		6	13.8	odd	4
5070.2.b.w.1351.6		6	13.5	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5070.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +4.80194 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +4.80194 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +2.55496 q^{11} +1.00000 q^{12} -4.80194 q^{14} -1.00000 q^{15} +1.00000 q^{16} -3.02715 q^{17} -1.00000 q^{18} -3.89977 q^{19} -1.00000 q^{20} +4.80194 q^{21} -2.55496 q^{22} -1.64310 q^{23} -1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{27} +4.80194 q^{28} +5.07606 q^{29} +1.00000 q^{30} +5.44504 q^{31} -1.00000 q^{32} +2.55496 q^{33} +3.02715 q^{34} -4.80194 q^{35} +1.00000 q^{36} +7.51573 q^{37} +3.89977 q^{38} +1.00000 q^{40} -5.89977 q^{41} -4.80194 q^{42} -10.1468 q^{43} +2.55496 q^{44} -1.00000 q^{45} +1.64310 q^{46} +6.42758 q^{47} +1.00000 q^{48} +16.0586 q^{49} -1.00000 q^{50} -3.02715 q^{51} -6.91185 q^{53} -1.00000 q^{54} -2.55496 q^{55} -4.80194 q^{56} -3.89977 q^{57} -5.07606 q^{58} +7.60925 q^{59} -1.00000 q^{60} +9.65279 q^{61} -5.44504 q^{62} +4.80194 q^{63} +1.00000 q^{64} -2.55496 q^{66} +0.929312 q^{67} -3.02715 q^{68} -1.64310 q^{69} +4.80194 q^{70} +14.9487 q^{71} -1.00000 q^{72} +14.1129 q^{73} -7.51573 q^{74} +1.00000 q^{75} -3.89977 q^{76} +12.2687 q^{77} -5.40581 q^{79} -1.00000 q^{80} +1.00000 q^{81} +5.89977 q^{82} +4.33513 q^{83} +4.80194 q^{84} +3.02715 q^{85} +10.1468 q^{86} +5.07606 q^{87} -2.55496 q^{88} -16.8267 q^{89} +1.00000 q^{90} -1.64310 q^{92} +5.44504 q^{93} -6.42758 q^{94} +3.89977 q^{95} -1.00000 q^{96} +17.9855 q^{97} -16.0586 q^{98} +2.55496 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 10 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 10 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 10 q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{10} + 8 q^{11} + 3 q^{12} - 10 q^{14} - 3 q^{15} + 3 q^{16} - 3 q^{17} - 3 q^{18} + 11 q^{19} - 3 q^{20} + 10 q^{21} - 8 q^{22} - 9 q^{23} - 3 q^{24} + 3 q^{25} + 3 q^{27} + 10 q^{28} + 3 q^{30} + 16 q^{31} - 3 q^{32} + 8 q^{33} + 3 q^{34} - 10 q^{35} + 3 q^{36} + 10 q^{37} - 11 q^{38} + 3 q^{40} + 5 q^{41} - 10 q^{42} - 3 q^{43} + 8 q^{44} - 3 q^{45} + 9 q^{46} + 3 q^{47} + 3 q^{48} + 17 q^{49} - 3 q^{50} - 3 q^{51} - 17 q^{53} - 3 q^{54} - 8 q^{55} - 10 q^{56} + 11 q^{57} + 11 q^{59} - 3 q^{60} + 11 q^{61} - 16 q^{62} + 10 q^{63} + 3 q^{64} - 8 q^{66} + 15 q^{67} - 3 q^{68} - 9 q^{69} + 10 q^{70} + 13 q^{71} - 3 q^{72} - q^{73} - 10 q^{74} + 3 q^{75} + 11 q^{76} + 29 q^{77} - 3 q^{79} - 3 q^{80} + 3 q^{81} - 5 q^{82} + 12 q^{83} + 10 q^{84} + 3 q^{85} + 3 q^{86} - 8 q^{88} + q^{89} + 3 q^{90} - 9 q^{92} + 16 q^{93} - 3 q^{94} - 11 q^{95} - 3 q^{96} - 6 q^{97} - 17 q^{98} + 8 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 10 * q^7 - 3 * q^8 + 3 * q^9 + 3 * q^10 + 8 * q^11 + 3 * q^12 - 10 * q^14 - 3 * q^15 + 3 * q^16 - 3 * q^17 - 3 * q^18 + 11 * q^19 - 3 * q^20 + 10 * q^21 - 8 * q^22 - 9 * q^23 - 3 * q^24 + 3 * q^25 + 3 * q^27 + 10 * q^28 + 3 * q^30 + 16 * q^31 - 3 * q^32 + 8 * q^33 + 3 * q^34 - 10 * q^35 + 3 * q^36 + 10 * q^37 - 11 * q^38 + 3 * q^40 + 5 * q^41 - 10 * q^42 - 3 * q^43 + 8 * q^44 - 3 * q^45 + 9 * q^46 + 3 * q^47 + 3 * q^48 + 17 * q^49 - 3 * q^50 - 3 * q^51 - 17 * q^53 - 3 * q^54 - 8 * q^55 - 10 * q^56 + 11 * q^57 + 11 * q^59 - 3 * q^60 + 11 * q^61 - 16 * q^62 + 10 * q^63 + 3 * q^64 - 8 * q^66 + 15 * q^67 - 3 * q^68 - 9 * q^69 + 10 * q^70 + 13 * q^71 - 3 * q^72 - q^73 - 10 * q^74 + 3 * q^75 + 11 * q^76 + 29 * q^77 - 3 * q^79 - 3 * q^80 + 3 * q^81 - 5 * q^82 + 12 * q^83 + 10 * q^84 + 3 * q^85 + 3 * q^86 - 8 * q^88 + q^89 + 3 * q^90 - 9 * q^92 + 16 * q^93 - 3 * q^94 - 11 * q^95 - 3 * q^96 - 6 * q^97 - 17 * q^98 + 8 * q^99

Introduction

L-functions

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Database

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